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\begin{thebibliography}{10}
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\bibitem{andrews86}
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Peter~B. Andrews.
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\newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth
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  Through Proof}.
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\newblock Academic Press, 1986.
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\bibitem{church40}
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Alonzo Church.
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\newblock A formulation of the simple theory of types.
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\newblock {\em Journal of Symbolic Logic}, 5:56--68, 1940.
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\bibitem{coen92}
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Martin~D. Coen.
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\newblock {\em Interactive Program Derivation}.
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\newblock PhD thesis, University of Cambridge, November 1992.
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\newblock Computer Laboratory Technical Report 272.
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\bibitem{constable86}
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R.~L. Constable et~al.
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\newblock {\em Implementing Mathematics with the Nuprl Proof Development
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  System}.
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\newblock Prentice-Hall, 1986.
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\bibitem{felty91a}
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Amy Felty.
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\newblock A logic program for transforming sequent proofs to natural deduction
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  proofs.
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\newblock In Peter Schroeder-Heister, editor, {\em Extensions of Logic
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  Programming}, LNAI 475, pages 157--178. Springer, 1991.
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\bibitem{frost93}
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Jacob Frost.
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\newblock A case study of co-induction in {Isabelle HOL}.
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\newblock Technical Report 308, Computer Laboratory, University of Cambridge,
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  August 1993.
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\bibitem{gallier86}
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J.~H. Gallier.
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\newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
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  Proving}.
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\newblock Harper \& Row, 1986.
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\bibitem{mgordon-hol}
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M.~J.~C. Gordon and T.~F. Melham.
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\newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher
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  Order Logic}.
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\newblock Cambridge University Press, 1993.
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\bibitem{huet78}
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G.~P. Huet and B.~Lang.
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\newblock Proving and applying program transformations expressed with
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  second-order patterns.
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\newblock {\em Acta Informatica}, 11:31--55, 1978.
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\bibitem{alf}
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Lena Magnusson and Bengt {Nordstr\"{o}m}.
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\newblock The {ALF} proof editor and its proof engine.
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\newblock In Henk Barendregt and Tobias Nipkow, editors, {\em Types for Proofs
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  and Programs: International Workshop {TYPES '93}}, LNCS 806, pages 213--237.
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  Springer, published 1994.
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\bibitem{mw81}
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Zohar Manna and Richard Waldinger.
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\newblock Deductive synthesis of the unification algorithm.
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\newblock {\em Science of Computer Programming}, 1(1):5--48, 1981.
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\bibitem{martinlof84}
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Per Martin-L\"of.
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\newblock {\em Intuitionistic type theory}.
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\newblock Bibliopolis, 1984.
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\bibitem{milner78}
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Robin Milner.
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\newblock A theory of type polymorphism in programming.
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\newblock {\em Journal of Computer and System Sciences}, 17:348--375, 1978.
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\bibitem{milner-coind}
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Robin Milner and Mads Tofte.
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\newblock Co-induction in relational semantics.
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\newblock {\em Theoretical Computer Science}, 87:209--220, 1991.
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\bibitem{Naraschewski-Wenzel:1998:TPHOL}
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Wolfgang Naraschewski and Markus Wenzel.
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\newblock Object-oriented verification based on record subtyping in
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  higher-order logic.
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\newblock In Jim Grundy and Malcolm Newey, editors, {\em Theorem Proving in
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  Higher Order Logics: {TPHOLs} '98}, LNCS 1479, pages 349--366, 1998.
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\bibitem{nazareth-nipkow}
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Dieter Nazareth and Tobias Nipkow.
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\newblock Formal verification of algorithm {W}: The monomorphic case.
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\newblock In von Wright et~al. \cite{tphols96}, pages 331--345.
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\bibitem{Nipkow-CR}
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Tobias Nipkow.
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\newblock More {Church-Rosser} proofs (in {Isabelle/HOL}).
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\newblock In Michael McRobbie and John~K. Slaney, editors, {\em Automated
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  Deduction --- {CADE}-13 International Conference}, LNAI 1104, pages 733--747.
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  Springer, 1996.
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\bibitem{nipkow-IMP}
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Tobias Nipkow.
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\newblock Winskel is (almost) right: Towards a mechanized semantics textbook.
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\newblock In V.~Chandru and V.~Vinay, editors, {\em Foundations of Software
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  Technology and Theoretical Computer Science}, volume 1180 of {\em LNCS},
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  pages 180--192. Springer, 1996.
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\bibitem{nordstrom90}
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Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith.
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\newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}.
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\newblock Oxford University Press, 1990.
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\bibitem{paulson85}
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Lawrence~C. Paulson.
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\newblock Verifying the unification algorithm in {LCF}.
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\newblock {\em Science of Computer Programming}, 5:143--170, 1985.
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\bibitem{paulson87}
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Lawrence~C. Paulson.
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\newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}.
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\newblock Cambridge University Press, 1987.
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\bibitem{paulson-CADE}
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Lawrence~C. Paulson.
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\newblock A fixedpoint approach to implementing (co)inductive definitions.
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\newblock In Alan Bundy, editor, {\em Automated Deduction --- {CADE}-12
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  International Conference}, LNAI 814, pages 148--161. Springer, 1994.
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\bibitem{paulson-set-II}
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Lawrence~C. Paulson.
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\newblock Set theory for verification: {II}. {Induction} and recursion.
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\newblock {\em Journal of Automated Reasoning}, 15(2):167--215, 1995.
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\bibitem{paulson-ns}
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Lawrence~C. Paulson.
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\newblock Mechanized proofs of security protocols: {Needham-Schroeder} with
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  public keys.
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\newblock Technical Report 413, Computer Laboratory, University of Cambridge,
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  January 1997.
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\bibitem{paulson-coind}
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Lawrence~C. Paulson.
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\newblock Mechanizing coinduction and corecursion in higher-order logic.
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\newblock {\em Journal of Logic and Computation}, 7(2):175--204, March 1997.
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\bibitem{paulson-security}
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Lawrence~C. Paulson.
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\newblock Proving properties of security protocols by induction.
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\newblock In {\em 10th Computer Security Foundations Workshop}, pages 70--83.
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  IEEE Computer Society Press, 1997.
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\bibitem{isabelle-ZF}
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Lawrence~C. Paulson.
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\newblock {Isabelle}'s logics: {FOL} and {ZF}.
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\newblock Technical report, Computer Laboratory, University of Cambridge, 1999.
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\bibitem{paulson-COLOG}
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Lawrence~C. Paulson.
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\newblock A formulation of the simple theory of types (for {Isabelle}).
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\newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88:
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  International Conference on Computer Logic}, LNCS 417, pages 246--274,
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  Tallinn, Published 1990. Estonian Academy of Sciences, Springer.
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\bibitem{pelletier86}
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F.~J. Pelletier.
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\newblock Seventy-five problems for testing automatic theorem provers.
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\newblock {\em Journal of Automated Reasoning}, 2:191--216, 1986.
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\newblock Errata, JAR 4 (1988), 235--236 and JAR 18 (1997), 135.
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\bibitem{plaisted90}
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David~A. Plaisted.
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\newblock A sequent-style model elimination strategy and a positive refinement.
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\newblock {\em Journal of Automated Reasoning}, 6(4):389--402, 1990.
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\bibitem{slind-tfl}
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Konrad Slind.
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\newblock Function definition in higher-order logic.
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\newblock In von Wright et~al. \cite{tphols96}.
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\bibitem{takeuti87}
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G.~Takeuti.
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\newblock {\em Proof Theory}.
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\newblock North-Holland, 2nd edition, 1987.
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\bibitem{thompson91}
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Simon Thompson.
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\newblock {\em Type Theory and Functional Programming}.
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\newblock Addison-Wesley, 1991.
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\bibitem{tphols96}
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J.~von Wright, J.~Grundy, and J.~Harrison, editors.
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\newblock {\em Theorem Proving in Higher Order Logics: {TPHOLs} '96}, LNCS
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  1125, 1996.
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\bibitem{winskel93}
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Glynn Winskel.
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\newblock {\em The Formal Semantics of Programming Languages}.
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\newblock MIT Press, 1993.
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\end{thebibliography}